Question: Rewrite as a simplified fraction. ${2.43\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2436.6666...\\ 100x &= 243.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2193}$ ${x = \dfrac{2193}{900}} $ ${x = \dfrac{731}{300}} \text{or} {2 \dfrac{131}{300}}$